1. Modeling Scheduling Problems
Agenda
Overview of Models
Notation
Objectives
Machine Configurations
Processing Characteristics
Constraints
12/7/2018
Sequencing and Scheduling

2. Overview of models Project Scheduling Job Shop Scheduling
precedence constraints
minimize makespan
critical tasks can be identified
Job Shop Scheduling

3. Overview of models Job Shop Scheduling Flexible Manufacturing Systems
minimize makespan or no of tardy jobs
Mostly for make-to-order manufacturing systems
Also in services
Flexible Manufacturing Systems
An automated material handling system controls the movement of jobs
Mostly for mass production systems
Maximize throughput

4. Overview of models Lot Scheduling Reservation Systems
Switching between products incurs a setup cost
Minimize total inventory and setup costs
Process industries, e.g. oil refinery, paper mill
Reservation Systems
Job start and complete times are fixed
Decide to process the job or not
Maximize no of jobs processed or utilization
Services, e.g. hotels, car rental agencies.

5. Overview of models Timetabling Workforce Scheduling
Certain jobs use the same equipment and cannot be processed at the same time
Minimize makespan
Examples: repair shops, classroom scheduling
Workforce Scheduling
Assign personnel to shifts
Constraints due to equipment requirements and work rules
Minimize no of employees or total cost

6. Notation Model representation:
Machine Configuration | Constraints | Objectives

7. Notation- Completion time
Resources 1 1 4 2 3 2 4 1 2 3 3 3 4 1 2 C4 C1
C2, C3
Time

8. Objectives Flowtime Time job j spends in the system
Flow time: Fj = Cj - rj
1) Minimize average flowtime
2) Minimize maximum flowtime

9. Objectives Throughput Makespan
Flow shop models or continuous processes
Bottleneck machines determine output rate
1) Maximize utilization of the bottleneck
2) Minimize sum of sequence-dependent setups
Makespan
Determined by the last completed job
Cmax = max(C1, C2, …, Cn )

10. Objectives Due Date Related Objectives 1) Minimize maximum lateness
Lateness of job j:
Maximum lateness:
2) Minimize number of tardy jobs
Tardiness of job j:
Objective function:
3) Minimize total weighted tardiness:

11. Objectives-due date related
Lateness of a job Tardiness of a job Lj Tj dj Cj dj Cj

12. Objectives Minimizing Total Cost 1) Setup Costs 2) WIP Inventory Costs
min WIP min throughput time min mean flowtime
3) Finished Goods Inventory Costs
4) Personnel Costs
Minimizing Total Earliness (JIT)
Maximizing Robustness

13. Machine Configurations
Single-Machine Parallel-Machine

14. Machine Configurations
Flow Shop
Job Shop

15. Processing Characteristics
Sequence-Dependent Setup Times and Costs
Length of setup depends on jobs
: setup time for processing job k after job j on machine i
Costs: waste of material, labor
Preemptions
Interrupt the processing of a job to process another one with higher priority

16. Constraints Precedence Constraints Routing Constraints
Precedence-constraints graph contains no cycles
Routing Constraints
Specifies a sequence of operations for each job and the machines at which these operations must be processed

17. Constraints Material Handling Constraints Storage Space Constraints
Machine Eligibility
Tooling and Resource
Personnel
Completion
time
Start time
Buffer Space
Jobs
Machines